Topology of U(2; 1) Representation Spaces
نویسنده
چکیده
We calculate the Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U (2; 1) and S U (2; 1). In order to obtain our results we use the identiication of this space with an appropriate mod-uli space of Higgs bundles and Morse theory, following Hitchin's programme 11]. This requires a careful analysis of critical subman-ifolds which turn out to have a description using either symmetric products of the surface or moduli spaces of Bradlow pairs.
منابع مشابه
N ov 2 00 2 TOPOLOGY OF U ( 2 , 1 ) REPRESENTATION SPACES
The Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U(2, 1) and SU(2, 1) are calculated. The results are obtained using the identification of these moduli spaces with moduli spaces of Higgs bundles, and Morse theory, following Hitchin’s programme [14]. This requires a careful analysis of critical submanifolds which turn out to ...
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تاریخ انتشار 2000